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An earthquake-produced surface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.60 $\mathrm{Hz}$ (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground?[Hint: Set the acceleration $a>g . ]$
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Physics 101 Mechanics
Physics 102 Electricity and Magnetism
Chapter 15
Wave Motion
Periodic Motion
Mechanical Waves
Electromagnetic Waves
Cornell University
Rutgers, The State University of New Jersey
Hope College
University of Winnipeg
Lectures
03:40
In physics, electromagnetic radiation (EM radiation or EMR) refers to the waves (or their quanta, photons) of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays. Electromagnetic waves of different frequency are called by different names since they have different sources and effects on matter. In order of increasing frequency and decreasing wavelength these are: radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays.
10:59
In physics, Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. They underpin all electric, optical and radio such electromagnetic technologies as power generation, electric motors, wireless communication, cameras, televisions, computers, and radar. Maxwell's equations describe how electric and magnetic fields are generated by charges, currents, and changes of these fields. The equations have two major variants. The microscopic Maxwell equations have universal applicability but are unwieldy for common calculations. They relate the electric and magnetic fields to total charge and total current, including the complicated charges and currents in materials at the atomic scale. The macroscopic Maxwell equations define two new auxiliary fields that describe the large-scale behaviour of matter without having to consider atomic scale details. The equations were published by Maxwell in his 1864 paper "A Dynamical Theory of the Electromagnetic Field". In the original paper Maxwell fully derived them from the Lorentz force law (without using the Lorentz transformation) and also from the conservation of energy and momentum.
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So here we have a sinus audio Transbourse way and for here we know that the frequency is point six zero hurts and this is going to be equal to omega over to pie. So we can say that a max is going to be equal to K A over M and that's getting people to omega squared times A. And this has to be greater than G because if we have ah, maximum acceleration that is greater than G. That means that the ground would fall quicker than the object which is here what we want. We want the we want the object to be suspended, want to adjust to being free fall because on its way down the ground, in fact should be falling falling quicker than the object. And this will only occur when the maximum acceleration is greater than the acceleration due to gravity. And so solving for amplitude we have The amplitude is greater than G over omega squared. So we can say that this is going to be equal. Teo g over four pi squared square and so the amplitude is going to be greater than nine point eight divided by four pi squared times point six squared. And so we get that amplitude is greater than point six nine meters. This would be our final answer. That is the end of the solution. Thank you for watching.
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